Definition df-iedg 16173

Description: Define the function mapping a graph to its indexed edges. This definition is very general: It defines the indexed edges for any ordered pair as its second component, and for any other class as its "edge function". It is meaningful, however, only if the ordered pair represents a graph resp. the class is an extensible structure (containing a slot for "edge functions") representing a graph. (Contributed by AV, 20-Sep-2020.)

Assertion

Ref	Expression
df-iedg	|- iEdg = ( g e. _V |-> if ( g e. ( _V X. _V ) , ( 2nd ` g ) , (.ef ` g ) ) )

Detailed syntax breakdown of Definition df-iedg

Step	Hyp	Ref	Expression
1		ciedg 16171	. 2 class iEdg
2		vg	. . 3 setvar g
3		cvv 2821	. . 3 class _V
4	2	cv 1401	. . . . 5 class g
5	3, 3	cxp 4770	. . . . 5 class ( _V X. _V )
6	4, 5	wcel 2209	. . . 4 wff g e. ( _V X. _V )
7		c2nd 6366	. . . . 5 class 2nd
8	4, 7	cfv 5375	. . . 4 class ( 2nd ` g )
9		cedgf 16162	. . . . 5 class .ef
10	4, 9	cfv 5375	. . . 4 class (.ef ` g )
11	6, 8, 10	cif 3638	. . 3 class if ( g e. ( _V X. _V ) , ( 2nd ` g ) , (.ef ` g ) )
12	2, 3, 11	cmpt 4190	. 2 class ( g e. _V |-> if ( g e. ( _V X. _V ) , ( 2nd ` g ) , (.ef ` g ) ) )
13	1, 12	wceq 1402	1 wff iEdg = ( g e. _V |-> if ( g e. ( _V X. _V ) , ( 2nd ` g ) , (.ef ` g ) ) )

This definition is referenced by:  iedgvalg  16175  edgval  16218